A Curry-Howard Approach to Church's Synthesis
Logic in Computer Science
2023-06-22 v4
Abstract
Church's synthesis problem asks whether there exists a finite-state stream transducer satisfying a given input-output specification. For specifications written in Monadic Second-Order Logic (MSO) over infinite words, Church's synthesis can theoretically be solved algorithmically using automata and games. We revisit Church's synthesis via the Curry-Howard correspondence by introducing SMSO, an intuitionistic variant of MSO over infinite words, which is shown to be sound and complete w.r.t. synthesis thanks to an automata-based realizability model.
Keywords
Cite
@article{arxiv.1803.08958,
title = {A Curry-Howard Approach to Church's Synthesis},
author = {Cécilia Pradic and Colin Riba},
journal= {arXiv preprint arXiv:1803.08958},
year = {2023}
}